In a 'Jason meets Percy' fanfic, they could meet in a place that is neutral to both of them, like a magical marketplace. Percy is there looking for a special item for his next adventure, and Jason is on a mission to find a way to strengthen his camp. They cross paths and initially have a bit of a misunderstanding. But as they start talking, they find out they have a common enemy in the background planning something big. So they decide to join forces and use their unique skills to stop the enemy.
A group of rogue demigods could be the antagonists. They are jealous of Percy and Jason's fame and power. They form a secret alliance and start causing trouble for the other demigods. Percy and Jason meet while trying to figure out who is behind these attacks. At first, they suspect each other, but then they realize the real culprits are this group of rogue demigods and join forces to stop them.
Maybe in the fanfic, there is a tournament in their world, and Jason and Percy are both participants. Before the actual tournament, they decide to spar with each other to test their mettle. Along the way, they face some challenges like disagreements on the rules of sparring or external distractions, but they work through them.
One idea could be that they team up to face a new and powerful monster that neither of them could defeat alone. Maybe it's a hybrid of a Greek and Roman mythical beast.
One possibility is that the gods see Percy and Jason as threats to their power. Maybe they've become too powerful or popular among the demigods. So, the gods plot against them in secret. They could set up a series of seemingly impossible challenges that are actually traps. Eventually, Percy and Jason fall into these traps and are killed. This could lead to chaos among the demigods as they lose two of their most powerful leaders.
Perhaps they argue over a girl. They are both heroes and might have feelings for the same person. Jealousy and competition could spark an argument between them. Also, their loyalty to different camps, Camp Half - Blood and Camp Jupiter, could be a source of conflict. They might have different ideas on how to handle the relationship between the two camps, which would lead to arguments.
One possible plot twist could be that Percy is initially oblivious to Jason's feelings. Then, just when Jason is about to give up, Percy discovers his own hidden feelings for Jason. Another twist could be that there's some external force, like a god or a prophecy, that tries to keep them apart. Or perhaps Jason discovers that Percy has a pre - existing relationship that he didn't know about, which complicates his crush.
Another possible plot twist is that their sparring somehow awakens an ancient prophecy. They initially think it's just a normal sparring session, but then strange signs start to appear. For example, old symbols start to glow on the ground around them as they spar. They then have to figure out what this prophecy means and how their sparring is related to it, all while still dealing with their friendly competition.
One idea could be that Jason is jealous of Percy's popularity among the demigods. So, he tries to outdo Percy in various quests, leading to some friendly competition that eventually turns into a real understanding between them. For example, there could be a big quest to retrieve a powerful artifact, and both Jason and Percy are chosen. Jason, being jealous, initially tries to take the lead all the time but realizes that Percy's skills are also valuable and they end up working together successfully.
One possible plot could be that they meet in a dangerous situation, like a new threat emerging in the demigod world. Maybe they have to team up to fight a powerful monster. Percy's experience with the sea could be combined with Jason's leadership and Leo's mechanical skills to come up with a unique plan to defeat the enemy.
At first, it might show the tension between them due to Jason's jealousy. Jason could be distant or snippy with Percy. But as the story progresses, they might start to communicate. Maybe Percy notices Jason's jealousy and tries to reach out, which begins to thaw the ice between them.